Honestly, I don't like it. At first I thought it was a short, sort of binary (at least machine-readable) representation of coordinates. A,A might be (0,0) in our coordinate system. Turns out it's not. It's not even global but country (or in the US, state) specific.
This means that the locations are controlled by a single entity together with country codes. Sure, postal codes are controlled by a single entity too, but at least they are regulated by the government using tax money instead of an arbitrary self-appointed committee.
I know it's meant to replace postal codes and not coordinates, but I'd like to see something that actually represents a place instead of an arbitrarily shaped region. OpenStreetMap's homepage happens to do this for their short URLs: http://osm.org/go/0GFeWn2RJ
Try moving on the OpenStreetMap map with the share menu opened and the short URL option selected. You'll see how it influences the short URL.
But anyway, back to replacing postal codes: the main advantage of this is that it'd be a universal and short code. In The Netherlands you could specify: NL 6114HT 41 and you'd have house number 41 at the Marktstraat (market street) in Susteren (city). Not much longer. And with this new system you'd still need to look up country-specific codes so I don't see much of an advantage.